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Special Relativity

https://www.howstuffworks.com/hsw-contact.htm (2000). How Special Relativity Works. [online] HowStuffWorks. Available at: https://science.howstuffworks.com/science-vs-myth/everyday-myths/relativity.htm.

  • Relativity is often referred to in sci-fi, eg Star Trek

    • Fiction to research:

      • Dr Who

      • Star Trek

      • Interstellar

    • “Space-time continuum”, “time dilation”, “wormholes”

  • Space and time are intertwined

    • Space is where everything exists

    • Time is a 4th dimension: it, along with space, are required to define an event happening

    • The reliance of space on time, and time on space, is known as the spacetime continuum

      • Any occurrence in our universe is an event of Space and Time

  • Special relativity removes the need for a universal time

    • Spacetime removes the idea of anything being able to happen simultaneously

  • Motion is where matter is changing its position in space

  • Mass is defined as how much matter an object contains

    • Total number of electrons, protons and neutrons

    • Multiply by the Earth’s gravity to get weight

    • Independent of position in space

    • Mass can also be defined as the amount of force required to cause an object to accelerate

      • Changes, but only to an observer, when in motion

  • Energy is a measure of a system’s ability to do something

    • Potential/kinetic etc

    • Energy can not be created or destroyed, only converted

  • Light is a form of energy

  • All motion is relative to the frame of reference

    • There is no absolute frame of reference, because everything is moving

    • If object A is standing still on Earth and object B is coming towards them:

      • From A’s perspective: B is moving towards them

      • From B’s perspective: A is moving towards them

      • Both are correct

  • Special relativity postulates the following:

    • The laws of physics hold true for all frames of reference

    • The speed of light is a constant in all frames of reference

      • Other velocities, such as movement of the object that the light is emitted from, do not affect it

      • If the Earth is travelling towards a light source then you would expect the light to be travelling faster than if it was coming from behind the Earth. However, both would actually be the same speed, even relative to Earth’s frame of reference

  • If you are on a moving object and you shoot a beam upwards and it reflects back, it will take less time for you than for an observer who is stationary

    • If you and the light source are moving at 90% of the speed of light and it takes 1 second for the light to go up and reflect back to you, then it would take a stationary observer 2.29 seconds for the light to go up and back down

    • Because from the stationary observer’s perspective the light is travelling at an angle, which is a longer distance than the straight lines up and down that you would perceive

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Hawking, S. (1996). A brief history of time. New York: Bantam Books.

  • Aristotle believed that the natural state of a body was at rest and that something would only move if driven by a force

  • Aristotle also stated that everything could be worked out by pure thought; observation was unnecessary

  • Galileo established the idea of performing experiments to test theories

    • Newton used his measurements to construct his laws of motion

  • Newton still believed in absolute time

  • In 1676 it was discovered that light travels at a finite speed

    • Discovered by observing that the moons of Jupiter were not orbiting Jupiter at a constant rate, as they should be, and were appearing to us at slightly different times than expected throughout the year. It was found that this was due to the distance between Earth and Jupiter being bigger at certain points in their orbits than at other points, so light from the moons took longer to get to Earth

  • It was assumed that light travelled through an ether and that its speed, relative to the ether, was constant and that it changed relatively to different observers

    • Eg the speed of light relative to an object moving towards it would be more than one moving away

    • Disproved by the Michelson-Morley experiment, in 1887, in which they compared the speed of light in the direction of the Earth’s motion with that at right angles to the Earth’s motion. They found them to be the same

  • Einstein introduced a new idea which removed the need for an ether

  • Theory of relativity removed the idea of absolute time

  • According to Special Relativity, nothing can travel faster than the speed of light, because to do so would require infinite energy because E=mc^2

  • Time is now used to calculate distance more accurately

    • By shooting a beam at the destination and calculating how long it takes to go there and reflect back. The distance would be half of that time multiplied by the speed of light

  • Space and time diagrams can be used to represent where and when an event happens in space and time

    • If you make the graph 3-dimensional (by plotting space on the x and z axes, with time on the y) then you can represent the cone of light that expands away from the event as time goes on. Everything within the cone is in the future of the event, while everything outside of it is called “elsewhere of the event”

      • The Earth does not enter the future light cone of the Sun until after 8 minutes

    • You can also plot the past light cone which shrinks as it gets towards the event

    • For any event ever in the universe we can construct an identical light cone like this, according to special relativity

  • Special relativity does not account for the Newtonian theory of gravity

  • Notes continued in “General Relativity” section

 

Rosser, W. G. V. (1967) Introductory relativity. London: Butterworths.

  • A second, according to the international bureau of weights and measures, is 1/31,556,925.9747 of the tropical year 1900

  • The theory of special relativity does not give numerical values of quantities in different frames of reference

    • It simply says that the laws of physics are the same in all inertial frames of reference

    • It also states that the speed of light, in empty space, is also constant in all inertial frames of reference

  • Some theories, such as Newtonian mechanics, obey the first postulate of special relativity but they do not account for a constant speed of light

 

 

 

 

 

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  • (See above) As the observer at ’ is travelling at 30% the speed of light they shoot the lamp upwards. Because the lamp is also travelling at the same speed the beam appears, in that frame of reference, to go straight up and down

    • However, for the observer at , who is observing the same light but from a stationary point, the light appears to travel up and down at angles. As the speed of light is constant but the distance travelled, because the angled lines are longer than those observed by ’, is longer then the time taken must also be longer

  • The clock paradox

    • There are two clocks, A and B. Clock A is on a spaceship and clock B is at rest on Earth. If the spaceship, containing A, leaves Earth and returns then clock A will read less time having passed than clock B. This is because of time dilation

    • Also known as the twin paradox

 

published, P.S. (2022). The ‘twin paradox’ shows us what it really means for time to be relative. [online] Space.com. Available at: https://www.space.com/time-is-relative-twin-paradox.

  • Both twins will disagree on the amount of time that has taken place for the other twin

    • The twin on Earth only becomes correct when the twin in changes from an inertial frame of reference (moving away from Earth) to turning and then to another inertial frame of reference (moving back to Earth)

  • The lost time, for the spaceship twin, is put into traversing spacetime

IMG_1359.heif

General Relativity

Arvin Ash (2020). General Relativity Explained simply & visually. YouTube. Available at: https://www.youtube.com/watch?v=tzQC3uYL67U.

  • Special relativity theory was rejected

    • Einstein was also unhappy with it as it did not account for gravity

  • Began as a thought experiment

    • Imagined being in a room with no windows and a scale

    • Then in the same room on a spaceship accelerating at 9.8m/s^2

    • The balance would measure the same

      • No way of knowing if they are in space or on Earth

    • By shooting a light, from a flashlight, from one end of the room in the spaceship to the other it is clear that the resulting light beam would curve downwards, because the room is accelerating upwards

      • Because of the law of equivalence this must be the same for the light on Earth, due to the force of gravity

    • Therefore, light must bend in the presence of gravity

      • But light always takes the shortest path, which suggests that the shortest path is actually curved

        • The same as how the shortest path between 2 points on the surface of a sphere (eg. The Earth) is curved

      • This suggests that mass and energy can actually change the shape of space through gravity

  • Acted against the Newtonian theories of the time which stated that time was absolute and that gravity was a mysterious force acting on all objects

  • Einstein’s theory instead posits that gravity is what emerges from interactions between matter and space

    • “Space-time tells matter how to move. Matter tells space-time how to curve.” – John Wheeler

  • Proved by explaining Mercury’s orbit which has a precession

    • General relativity predicts the precession exactly

  • Tested and proved by scientists in 1919 who, during a solar eclipse, were able to see how the sun’s gravity affected light from stars by making them be seen in places that they actually shouldn’t be

  • Time is affected by gravity

    • The speed of light is constant

    • As gravity causes space to curve around massive objects this causes the distance, to get from one side of the object to the other, to be longer than if the object was not there

    • Because speed = distance/time, and the speed of light is constant, the time has to increase along with the distance

  • Observer of time from space experiences time differently to one in a gravitational field

    • Space stations and satellites have to adjust their times accordingly to ensure that GPS info works correctly

 

Hawking, S. (1996). A brief history of time. New York: Bantam Books.

  • According to Newtonian mechanics the force of gravity applies instantaneously to all objects. This means that gravitational effects should travel at infinite velocity, which didn’t fit with the theory of Special Relativity

  • Einstein’s theory of General Relativity suggested, instead, that gravity was not a force like the others and instead it curves space-time which was originally presumed to be flat

    • Established in 1915, 10 years after SR

    • The curve then results in everything travelling on it to actually be travelling the closest thing to a straight line as it can

  • There is a relation between the energy of light and its frequency

    • Greater energy = higher frequency

    • It requires energy to move up in a gravitational field so light from below would always appear to have a lower frequency to someone observing above

      • Therefore to the observer above, time would appear to pass slower below them

 

Geroch, R. (1978) General relativity from a to b. Chicago: University of Chicago Press.

  • M can be used to denote the set of all events in spacetime

    • An event is something that occurs in the universe

  • In the set M a particle existing in the universe would be represented as a line (as it moves through space and time)

    • This is known as the world-line of the particle

    • A collision between 2 particles would be shown as the two lines crossing

  • The Aristotelian view establishes that time and space are absolute and one could describe any event in terms of x, y, z and t (time) and it would only ever describe that event

    • By this view any event where x, y, z and t is equal to those of another event then the two events must be the same event

    • An issue with this view is that it does not account for the observer

      • An observer may need to define the x, y and z of a particle between two times, however, the observer may be moving at a constant velocity, which they cannot measure, and happen to be moving at the same velocity as the particle. From the observers perspective, then, the particle would be stationary and their x, y and z coordinates would not have changed

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